Assume stably stratified fluid but not in equilibrium, e.g. with non-constant temperature gradient for example. Can convection cells be present? Typical example of convection cells is Rayleigh–Bénard convection. But this is example of unstably stratified fluid. In stably stratified fluid which is not in equilibrium is there some mechanism introducing instability? I'm targeting to low viscosity and very high externally-induced heat flux.
You may want to go over the paper 'Electrohydrodynamic Convection' by P H Roberts. The paper's abstract begins with - "Experiments have been performed by Gross in which a layer of insulating oil is confined between horizontal conducting planes, spaced at a distance d, and is heated from above and cooled from below. When a vertical electric field E of sufficient strength is applied across the layer, a tessellated pattern of motions is observed which, despite the fact that buoyancy is here stabilizing, is strikingly similar to that characteristic of Be'nard convection."